Lindbladians for controlled stochastic Hamiltonians
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| Lizenz | CC-Namensnennung 3.0 Unported: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. | |
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Transkript: Englisch(automatisch erzeugt)
00:03
Hi, my name is Michael and I'm going to tell you a little bit about our article, the Bladians for controlled stochastic Hamiltonians. Suppose you want to compare two schemes for dynamic decoupling, for example bang-bang with spin-locking. How would you go about it?
00:21
You could do an experiment, a simulation, or make a theory that outputs the phasing rates. Ideally, you'd want to do all three and check that they agree. Here, we construct an analytical framework that outputs the phasing rates and tests it against simulations. The phasing rates are the byproduct of the construction of Lindbladians.
00:43
The framework for constructing Lindbladians from Hamiltonian evolutions is weak coupling. In this work, we apply weak coupling to controlled stochastic evolutions. This is new and so are our expressions for the Lindbladians and the phasing rates.
01:01
The Hamiltonians we are considering involve stochastic noise and a deterministic control field whose purpose is to minimize the phasing. Each H-alpha is an independent noise type and the psi alphas are the corresponding stochastic noise amplitudes. The H-alphas are generally non-commuting, making the problem hard to solve analytically.
01:24
The psi are stationary Gaussian random processes that have a correlation function J that decays on a timescale tau. Weak coupling has epsilon as the small parameter. Small epsilon means that the phase acquired by the wave function during one correlation
01:41
time in the absence of control is small. So, let's come to the results. The evolution on the coarse-grained, slow timescale S of the density matrix rho averaged over all possible moist configurations is governed by a complete positivity-preserving
02:01
Lindbladian. The fact that the time evolution is Lindbladian is a feature of weak coupling and coarse-graining. For example, on short timescales, the evolution is not necessarily Markovian or a contraction. As you can see on the graph, on timescales similar to the noise correlation length, gamma, the rate of decoherence, can be negative, exemplifying the non-Markovity
02:25
of the evolution. The main result is an explicit construction of Lindbladians for controlled stochastic evolutions in the weak coupling limit. It's too complicated to explain in a minute, so let's see its application on some examples.
02:42
Going back to our initial goal, let us compare the bang-bang pulsed decoupling method, which means periodically applying party pulses to the system, and spin locking, which means applying a constant field, thus creating Rabi oscillations.
03:00
Taking the same control parameter for both, which means the frequency of pulses for bang-bang and the Rabi frequency for constant control, we can compare their efficiency and our theory to numerical simulations. We see that there is a good match between the Lindblad evolution and simulated evolution.
03:20
Note that these simulations are time-consuming and require failed sampling, which can be tricky. Several other examples are discussed in detail in the article. Among the possible applications of these results are noise spectrum determination via measurements of the phasing rates, dynamic decoupling control optimization, and testing
03:43
numerical algorithms. Thank you for your attention.